Lucien is Collignon the grocer's assistant. He has some sort of mental disability that causes him to be a little slower than others and to not understand some social cues.
Amélie likes Lucien's slow movements—"She likes the way he handles each endive like a precious object, to be treated with care. It's his way of showing his love of good work." Collignon, however, calls him "spastic," which is the European equivalent of calling someone the r-word.
Despite the verbal and sometimes physical abuse, Lucien stays employed by Collignon. Lucien always has a happy demeanor, and he's a promising painter, even if (like the actor who plays him) he does only have the use of one arm. When he does grocery delivery to Dufayel, he hides luxury foods like caviar on the tray, and we wouldn't be surprised if these little excesses were coming out of Collignon's pocket. Dufayel likes to see Lucien getting him back in small ways.
Perhaps because of his developmental disability, Lucien is obsessed with Lady Diana. Collignon rudely reveals to the customers that Lucien taped her face to some models in a lingerie catalog, and even Dufayel gets sick of Lucien's obsession at one point, yelling at him to stop obsessing about Princess Diana and just paint. Maybe Dufayel is yelling more at himself here, because he is almost as obsessed with Amélie as Lucien is with Princess Diana.